How Do You Make Geometry Proofs Shorter?
So you know how to write a geometry proof, but you have a burning desire to know how to make a geometry proof shorter. What, are you trying to play a mathematics version of the Six Degrees of Kevin Bacon? Learning how to make geometric proofs shorter requires you to have a encyclopedic understanding of geometric theorems, plus a good feel for how the theorems apply to proofs. Write a geometry theorem. You want one that has several steps, not something obvious. Alternatively you can find one somebody else has done and make them feel bad when you turn their clunky 16 step piece of junk into a lean 5 step mathematical miracle. For the sake of illustration, use the following proof: Given an equilateral triangle ABC, prove that a line DE that bisects two sides of the triangle must be parallel to the remaining side. Examine the reasoning behind each step of the proof. In the example, if a line bisects side AB and bisects side BC, one proof might involve first proving that a straight line dra
